Kriging techniques are suited well for evaluation of continuous, spatial phenomena. Bayesian statistics are characterized by using prior qualified guesses on the model parameters. By merging kriging techniques and Bayesian theory, prior guesses may be used in a spatial setting. Partial knowledge of model parameters defines a continuum of models between what is named simple and universal kriging in geostatistical terminology. The Bayesian approach to kriging is developed and discussed, and a case study concerning depth conversion of seismic reflection times is presented.